The Golgi apparatus (GA) is the main station along the secretory pathway. Mechanisms of intra-Golgi transport remain unresolved. Three models compete with each other for the right to be defined as the paradigm. The vesicular model cannot explain the following: (1) lipid droplets and aggregates of procollagen that are larger than coatomer I (COPI)-dependent vesicles are transported across the GA; and (2) most anterograde cargoes are depleted in COPI vesicles. The compartment progression/maturation model has the following problems: (1) most Golgi-resident proteins are depleted in COPI vesicles; (2) there are no COPI vesicles for the recycling of the resident proteins in the trans-most-Golgi cisterna; and (3) different proteins have different rates of intra-Golgi transport. The diffusion model based on permanent inter-cisternal connections cannot explain the existence of lipid, ionic and protein gradients across the Golgi stacks. In contrast, the kiss-and-run model has the potential to explain most of the experimental observations. The kiss-and-run model can be symmetric when fusion and then fission occurs in the same place, and asymmetric when fusion takes place in one location, whereas fission takes place in another. The asymmetric kiss-and-run model resembles the carrier maturation mechanism, and it can be used to explain the transport of large cargo aggregates.